EUDML

Let $(M, g)$ be a compact Riemannian manifold of dimension $n \geq 3$ .We suppose that $g$ is a metric in the Sobolev space $H_{2}^{p} (M, T^{*} M \otimes T^{*} M)$ with $p > \frac{n}{2}$ and there exist a point $P \in M$ and $δ > 0$ such that $g$ is smooth in the ball $B_{p} (δ)$ . We define the second Yamabe invariant with singularities as the infimum of the second eigenvalue of the singular Yamabe operator over a generalized class of conformal metrics to $g$ and of volume $1$ . We show that this operator is attained by a generalized metric, we deduce nodal solutions to a Yamabe type equation with...

Subalgebras of finite codimension in symplectic Lie algebra

Mohammed Benalili; Abdelkader Boucherif — 1999

Archivum Mathematicum

Subalgebras of germs of vector fields leaving $0$ fixed in $R^{2 n}$ , of finite codimension in symplectic Lie algebra contain the ideal of germs infinitely flat at $0$ . We give an application.

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On a class of non linear differential operators of first order with singular point.

A property of the ideals of finite codimension of the Lie algebras of vector fields. (Une propriété des idéaux de codimension finie des algèbres de Lie de champs de vecteurs.)

Ideals of finite codimension in contact Lie algebra.

Solving $p$ -Laplacian equations on complete manifolds.

Global stability of dynamic systems of high order.

Generalized scalar curvature type equation on complete Riemannian manifolds.

Spectral properties of the adjoint operator and applications.

The second Yamabe invariant with singularities

Subalgebras of finite codimension in symplectic Lie algebra